Designing Incidence-Angle-Targeted Anti-Cavitation Foil Profiles Using a Combination Optimization Strategy
Abstract
:1. Introduction
2. The Studied Hydrofoil Object
3. Methods
3.1. Numerical Model of Turbulent Flow
3.2. CFD Setup
3.3. Brief Introduction to the Diffusion Angle Integral Method
- Providing the long/short axis ratio Rab = aLE/bLE;
- Based on Rab, scaling the ellipse arc into an arc;
- Providing the diffusion angle γs and calculating the scaled LE arc rLE;
- Providing the thickness integral coefficient B (the change rate of Part 2 in Figure 4) and integrating the thickness diffusion part;
- Based on Rab, scaling the designed arc back to an ellipse arc.
3.4. Orthogonal Testing
4. Optimization
4.1. Global Dynamic Criterion Algorithm
4.2. Comparison of Foil Geometry
5. Results and Discussion
5.1. Comparison of −Cpmin and Lift/Drag Ratio
5.2. Pressure Distribution on the Foil Surface
5.3. Flow Field around the Foil
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
- Hammitt, F.G. Cavitation and Multiphases Flow Phenomena, 1st ed.; McGraw-Hill: New York, NY, USA, 1980; ISBN 9780070259072. [Google Scholar]
- Luo, X.; Ji, B.; Tsujimoto, Y. A review of cavitation in hydraulic machinery. J. Hydrodyn. 2016, 28, 335–358. [Google Scholar] [CrossRef]
- Pan, Z.Y.; Yuan, S.Q. Fundamentals of Cavitation in Pumps, 1st ed.; Jiangsu University Press: Zhenjiang, China, 2013. [Google Scholar]
- Bishop, R.J.; Totten, G.E. Effect of pump inlet conditions on hydraulic pump cavitation: A review. ASTM Spec. Tech. 2001, 339, 318–332. [Google Scholar]
- Lauterborn, W.; Bolle, H. Experimental investigation of cavitation-bubble collapse in the neighbourhood of a solid boundary. J. Fluid Mech. 1975, 72, 391–399. [Google Scholar] [CrossRef]
- Wang, G.; Liu, S.; Shintani, M. Study on Cavitation Damage Characteristics around a Hollow-Jet Valve. JSME Int. J. 1999, 42, 649–657. [Google Scholar] [CrossRef]
- Visser, F.C.; Backx, J.J.M.; Geerts, J. Pump impeller lifetime improvement through visual study of leading-edge cavitation. In Proceedings of the International Pump Users Symposium, Houston, TX, USA, 3–5 March 1998. [Google Scholar]
- Tao, R.; Xiao, R.; Zhu, D. Predicting the inception cavitation of a reversible pump-turbine in pump mode. In Proceedings of the 9th International Symposium on Cavitation, Lausanne, Switzerland, 6–10 December 2015. [Google Scholar]
- Ruan, H.; Luo, X.; Liao, W. Effects of low pressure edge thickness on cavitation performance and strength for pump-turbine. Trans. Chin. Soc. Agric. Eng. 2015, 31, 32–39. [Google Scholar]
- Adhikari, R.; Vaz, J.; Wood, D. Cavitation Inception in Crossflow Hydro Turbines. Energies 2016, 9, 237. [Google Scholar] [CrossRef]
- Anaka, T.; Tsukamoto, H. Transient behavior of a cavitating centrifugal pump at rapid change in operating conditions-Part 2: Transient phenomena at pump startup/shutdown. J. Fluids Eng. 1999, 121, 850–856. [Google Scholar]
- Balasubramanian, R.; Sabini, E.; Bradshaw, S. Influence of impeller leading edge profiles on cavitation and suction performance. In Proceedings of the 27th International Pump Users Symposium, Houston, TX, USA, 12–15 September 2011. [Google Scholar]
- Obeid, S.; Jha, R.; Ahmadi, G. RANS Simulations of Aerodynamic Performance of NACA 0015 Flapped Airfoil. Fluids 2017, 2, 2. [Google Scholar] [CrossRef]
- Wang, G.; Ostoja-Starzewski, M. Large eddy simulation of a sheet/cloud cavitation on a NACA0015 hydrofoil. Appl. Math. Model. 2007, 31, 417–447. [Google Scholar] [CrossRef]
- Neill, G.D.; Reuben, R.L.; Sandford, P.M. Detection of incipient cavitation in pumps using acoustic emission. J. Process. Mech. Eng. 1997, 211, 267–277. [Google Scholar] [CrossRef]
- Fukaya, M.; Okamura, T.; Tamura, Y. Prediction of cavitation performance of axial flow pump by using numerical cavitating flow simulation with bubble flow model. In Proceedings of the 5th International Symposium on Cavitation, Osaka, Japan, 1–4 November 2003. [Google Scholar]
- Barre, S.; Rolland, J.; Boitel, G. Experiments and modeling of cavitating flows in venturi: Attached sheet cavitation. Eur. J. Mech. B/Fluids 2009, 28, 444–464. [Google Scholar] [CrossRef]
- Acosta, A.J.; Tsujimoto, Y.; Yoshida, Y. Effects of leading edge sweep on the cavitating characteristics of inducer pumps. Int. J. Rotating Mach. 2007, 7, 397–404. [Google Scholar] [CrossRef]
- Numachi, F.; Oba, R.; Chida, I. Effect of surface roughness on cavitation performance of hydrofoils-report 1. J. Basic Eng. 1965, 87, 495–502. [Google Scholar] [CrossRef]
- Yao, Z.; Xiao, R.; Wang, F. Numerical investigation of cavitation improvement for a francis turbine. In Proceedings of the 9th International Symposium on Cavitation, Lausanne, Switzerland, 1–5 December 2015. [Google Scholar]
- Kinnas, S.A. Non-Linear Corrections to the Linear Theory for the Prediction of the Cavitating Flow around Hydrofoils. Ph.D. Thesis, Massachusetts Institute of Technology, Boston, MA, USA, 1985. [Google Scholar]
- Tao, R.; Xiao, R.; Farhat, M. Effect of leading edge roughness on cavitation inception and development on a thin hydrofoil. J. Drain. Irrig. Mach. Eng. 2017, 35, 921–926. [Google Scholar]
- Bouziad, Y.A. Physical modelling of leading edge cavitation: Computational methodologies and application to hydraulic machinery. EPFL 2005, 3353. [Google Scholar] [CrossRef]
- Ausoni, P. Turbulent vortex shedding from a blunt trailing edge hydrofoil. EPFL 2009. [Google Scholar] [CrossRef]
- Coutier-Delgosha, O.; Reboud, J.L.; Delannoy, Y. Numerical simulation of the unsteady behavior of cavitating flows. Int. J. Numer. Methods Fluids 2003, 42, 527–548. [Google Scholar]
- Kunz, R.F.; Boger, D.A.; Stinebring, D.R. A preconditioned Navier–Stokes method for twophase flows with application to cavitation prediction. Comput. Fluids 2000, 29, 849–875. [Google Scholar] [CrossRef]
- Yang, W.; Xiao, R.; Wang, F. Influence of splitter blades on the cavitation performance of a double suction centrifugal pump. Adv. Mech. Eng. 2014, 6. [Google Scholar] [CrossRef]
- Gopalan, S.; Katz, J. Flow structure and modeling issues in the closure region of attached cavitation. Phys. Fluids 2000, 12, 895–911. [Google Scholar] [CrossRef]
- Luo, X.; Zhang, Y.; Peng, J. Impeller inlet geometry effect on performance improvement for centrifugal pumps. J. Mech. Sci. Technol. 2008, 22, 1971–1976. [Google Scholar] [CrossRef]
- Tan, L.; Cao, S.; Wang, Y. Numerical Simulation of Cavitation in a Centrifugal Pump at Low Flow Rate. Chin. Phys. Lett. 2012, 29, 014702. [Google Scholar] [CrossRef]
- Ting, C.K. On the mean convergence time of multi-parent genetic algorithms without selection. Adv. Artif. Life 2005, 403–412. [Google Scholar]
- Akbari, R.; Ziarati, K. A multilevel evolutionary algorithm for optimizing numerical functions. Int. J. Ind. Eng. Comput. 2011, 2, 419–430. [Google Scholar] [CrossRef]
- Whitley, D. A genetic algorithm tutorial. Stat. Comput. 1994, 4, 65–85. [Google Scholar] [CrossRef]
- Colorni, A.; Dorigo, M.; Maniezzo, V. Ant system for job-shop scheduling. Oper. Res. Stat. Comput. Sci. 1994, 34, 39–53. [Google Scholar]
- Cormen, T.H.; Leiserson, C.E.; Rivest, R.L. Introduction to Algorithms, 2nd ed.; McGraw-Hill: New York, NY, USA, 2001. [Google Scholar]
- Huang, L.; Huang, P.G.; Lebeau, R.P. Optimization of aifoil flow control using a genetic algorithm with diversity control. J. Aircr. 2007, 44, 1337–1349. [Google Scholar] [CrossRef]
- Liu, H.; Wang, K.; Yuan, S. Multicondition Optimization and Experimental Measurements of a Double-Blade Centrifugal Pump Impeller. J. Fluids Eng. 2013, 135, 111031. [Google Scholar] [CrossRef] [PubMed]
- Liu, L.; Zhu, B.; Bai, L. Parametric design of an ultrahigh-head pump-turbine runner based on multiobjective optimization. Energies 2017, 10, 1169. [Google Scholar] [CrossRef]
- Liu, M.; Tan, L.; Cao, S. Design method of controllable blade angle and orthogonal optimization of pressure rise for a multiphase pump. Energies 2018, 11, 1048. [Google Scholar] [CrossRef]
- Tao, R.; Xiao, R.; Wang, F. Improving the cavitation inception performance of a reversible pump-turbine in pump mode by blade profile redesign: Design concept, method and applications. Renew. Energy 2019, 133, 325–342. [Google Scholar] [CrossRef]
- Behnia, M.; Parneix, S.; Shabany, Y. Numerical study of turbulent heat transfer in confined and unconfined impinging jets. Int. J. Heat Fluid Flow 1999, 20, 1–9. [Google Scholar] [CrossRef]
- Durbin, P.A. Separated Flow Computations with the k–ε–v2 Model. AIAA J. 1995, 33, 659–664. [Google Scholar] [CrossRef]
- Parneix, S.; Durbin, P.A.; Behnia, M. Computation of 3-D Turbulent Boundary Layers Using the V2F Model. Flow Turbul. Combust. 1998, 60, 19–46. [Google Scholar] [CrossRef]
Constant | α | C1 | C2 | Cε1 | Cε2 | Cη | Cμ | CL | σk | σε |
---|---|---|---|---|---|---|---|---|---|---|
Value | 0.6 | 1.4 | 0.3 | 1.4 | 1.9 | 70 | 0.22 | 0.23 | 1.0 | 1.3 |
Level | Factor | ||
---|---|---|---|
Rab | γs [degree] | B | |
1 | 1 | 1 | 1 |
2 | 1.5 | 2 | 2 |
3 | 2 | 3 | 3 |
4 | 2.5 | 4 | 4 |
5 | 3 | 5 | 5 |
Order Number | Rab | γs [deg] | B | Cp0 | Cp3 | Cp6 |
---|---|---|---|---|---|---|
1 | 1 | 1 | 1 | −1.4987 | −2.889 | −4.4240 |
2 | 1 | 2 | 2 | −1.4316 | −2.8391 | −4.4486 |
3 | 1 | 3 | 3 | −1.3561 | −2.8080 | −4.5451 |
4 | 1 | 4 | 4 | −1.2756 | −2.7677 | −4.5856 |
5 | 1 | 5 | 5 | −1.1910 | −2.7169 | −4.5187 |
6 | 1.5 | 1 | 2 | −1.0299 | −2.1063 | −3.5227 |
7 | 1.5 | 2 | 3 | −0.9875 | −2.0877 | −3.5436 |
8 | 1.5 | 3 | 4 | −0.9407 | −2.0723 | −3.5969 |
9 | 1.5 | 4 | 5 | −0.8888 | −2.0526 | −3.5870 |
10 | 1.5 | 5 | 1 | −0.8322 | −2.0367 | −3.6896 |
11 | 2 | 1 | 3 | −0.7890 | −1.7245 | −3.1430 |
12 | 2 | 2 | 4 | −0.7610 | −1.7185 | −3.1881 |
13 | 2 | 3 | 5 | −0.7299 | −1.7103 | −3.2384 |
14 | 2 | 4 | 1 | −0.6940 | −1.7091 | −3.2879 |
15 | 2 | 5 | 2 | −0.6526 | −1.7020 | −3.3610 |
16 | 2.5 | 1 | 4 | −0.6439 | −1.5140 | −3.0710 |
17 | 2.5 | 2 | 5 | −0.6262 | −1.5180 | −3.1082 |
18 | 2.5 | 3 | 1 | −0.6048 | −1.5189 | −3.1723 |
19 | 2.5 | 4 | 2 | −0.5783 | −1.5251 | −3.2313 |
20 | 2.5 | 5 | 3 | −0.5467 | −1.5277 | −3.3146 |
21 | 3 | 1 | 5 | −0.5469 | −1.4048 | −3.1355 |
22 | 3 | 2 | 1 | −0.5357 | −1.4083 | −3.1153 |
23 | 3 | 3 | 2 | −0.5216 | −1.4109 | −3.2224 |
24 | 3 | 4 | 3 | −0.5027 | −1.4163 | −3.2881 |
25 | 3 | 5 | 4 | −0.4768 | −1.4230 | −3.3829 |
ParamETERS | Cp0 | Cp3 | Cp6 | ||||||
---|---|---|---|---|---|---|---|---|---|
Rab | γs [deg] | B | Rab | γs [deg] | B | Rab | γs [deg] | B | |
K1 | −9.0567 | −6.3002 | −6.0576 | −14.144 | −9.8917 | −9.8353 | −20.095 | −15.252 | −15.524 |
K2 | −6.5729 | −6.1712 | −6.1082 | −10.546 | −9.8318 | −9.8667 | −15.855 | −15.314 | −15.609 |
K3 | −5.3795 | −6.0521 | −6.0855 | −8.8359 | −9.8091 | −9.8531 | −14.194 | −15.587 | −15.642 |
K4 | −4.7500 | −5.8966 | −6.0104 | −7.9727 | −9.7685 | −9.7886 | −13.778 | −15.725 | −15.619 |
K5 | −4.3877 | −5.7268 | −5.8853 | −7.5234 | −9.7216 | −9.6791 | −13.880 | −15.924 | −15.409 |
k1 | −1.8114 | −1.2601 | −1.2115 | −2.8289 | −1.9783 | −1.9671 | −4.0190 | −3.0503 | −3.1048 |
k2 | −1.3146 | −1.2342 | −1.2216 | −2.1093 | −1.9664 | −1.9733 | −3.1711 | −3.0629 | −3.1217 |
k3 | −1.0759 | −1.2104 | −1.2171 | −1.7672 | −1.9618 | −1.9706 | −2.8388 | −3.1175 | −3.1284 |
k4 | −0.9500 | −1.1793 | −1.2021 | −1.5945 | −1.9537 | −1.9577 | −2.7556 | −3.1450 | −3.1238 |
k5 | −0.8775 | −1.1454 | −1.1771 | −1.5047 | −1.9443 | −1.9358 | −2.7760 | −3.1848 | −3.0817 |
R | 0.9338 | 0.1147 | 0.0446 | 1.3242 | 0.0340 | 0.0375 | 1.2634 | 0.1345 | 0.0467 |
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Zhu, D.; Xiao, R.; Tao, R.; Wang, F. Designing Incidence-Angle-Targeted Anti-Cavitation Foil Profiles Using a Combination Optimization Strategy. Energies 2018, 11, 3099. https://doi.org/10.3390/en11113099
Zhu D, Xiao R, Tao R, Wang F. Designing Incidence-Angle-Targeted Anti-Cavitation Foil Profiles Using a Combination Optimization Strategy. Energies. 2018; 11(11):3099. https://doi.org/10.3390/en11113099
Chicago/Turabian StyleZhu, Di, Ruofu Xiao, Ran Tao, and Fujun Wang. 2018. "Designing Incidence-Angle-Targeted Anti-Cavitation Foil Profiles Using a Combination Optimization Strategy" Energies 11, no. 11: 3099. https://doi.org/10.3390/en11113099